Question

3. A sample of four claim amounts from a portfolio of insurance had values 3500, 2900,...

3. A sample of four claim amounts from a portfolio of insurance had values 3500, 2900, 2800, 2840

A suitable loss distribution for this data set is thought to be the Pareto distribution with pdf ?(?) = ? ×75? / (75+?)?+1 , ? > 0

a) Derive the cdf for this distribution. [4 marks]

b) Derive the mean for this distribution. [8 marks]

c) Find an express for the median of this distribution. [5 marks]

c) Find the methods of moments estimate of ?. [5 marks]

e) Find the maximum likelihood estimate of ?. [7 marks]

f) Find the method of percentiles estimate of ?. [6 marks]

[Total 35 marks]

math Statistics-And-Probability

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